Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance

Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance

We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with $l_2$ separation. We establish the minimax...

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Veröffentlicht in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2022-11
Hauptverfasser: Carpentier, Alexandra, Collier, Olivier, Comminges, Laëtitia, Tsybakov, Alexandre B., Wang, Yuhao
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Statistics
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container_title Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
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creator Carpentier, Alexandra
Collier, Olivier
Comminges, Laëtitia
Tsybakov, Alexandre B.
Wang, Yuhao
description We consider the related problems of estimating the $l_2$-norm and the squared $l_2$-norm in sparse linear regression with unknown variance, as well as the problem of testing the hypothesis that the regression parameter is null under sparse alternatives with $l_2$ separation. We establish the minimax optimal rates of estimation (respectively, testing) in these three problems.
doi_str_mv 10.3150/21-BEJ1436
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Statistics
title Estimation of the $l_2$-norm and testing in sparse linear regression with unknown variance
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